Sr Examen
Ecuación diferencial y'''-2*y''-8*y'=(4-x)*exp(4*x)+8*sin(4*x)-3*x
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Solución
Ha introducido
[src]
2 3
d d d 4*x
- 8*--(y(x)) - 2*---(y(x)) + ---(y(x)) = -3*x + 8*sin(4*x) + (4 - x)*e
dx 2 3
dx dx
$$- 8 \frac{d}{d x} y{\left(x \right)} - 2 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = - 3 x + \left(4 - x\right) e^{4 x} + 8 \sin{\left(4 x \right)}$$
-8*y' - 2*y'' + y''' = -3*x + (4 - x)*exp(4*x) + 8*sin(4*x)
Respuesta
[src]
2 / 2 \
3*x sin(4*x) 3*x 3*cos(4*x) -2*x | x 53*x| 4*x
y(x) = C1 - --- + -------- + ---- + ---------- + C3*e + |C2 - -- + ----|*e
32 40 16 40 \ 48 288 /
$$y{\left(x \right)} = C_{1} + C_{3} e^{- 2 x} + \frac{3 x^{2}}{16} - \frac{3 x}{32} + \left(C_{2} - \frac{x^{2}}{48} + \frac{53 x}{288}\right) e^{4 x} + \frac{\sin{\left(4 x \right)}}{40} + \frac{3 \cos{\left(4 x \right)}}{40}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth order reducible
nth linear constant coeff variation of parameters Integral